This book explores the intersection of particle physics, astrophysics, and cosmology known as astroparticle physics. Extreme electromagnetic conditions present in puslars and other stars allow for investigations of the role of quantum processes in the dynamics of astrophysical objects and in the early Universe. Based in part on the authors' own work, this book systematically describes several methods of calculation of the effects of strong electromagnetic fields in quantum processes using analytical solutions of the Dirac equation and Feynmann diagrams at both the loop and tree levels. The consideration is emphasized at the two limiting cases: the case of a very strong magnetic field, and the case of a crossed field. The presentation will appeal to graduate students of theoretical physics with prior understanding of Quantum Field Theory (QFT) and the Standard Model of Electroweak Interactions, as well as specialists in QFT wishing to know more about the problems of quantum phenomena in external electomagnetic fields.